A261311 Fixed points of sequence A262211 which yields the minimum number of 12's such that [n; 12, ..., 12, n] = [x; ..., x] for some x; [...] being continued fractions.

19, 23, 31, 43, 59, 79, 103, 163, 179, 199, 227, 239, 251, 283, 331, 347, 383, 431, 439, 463, 467, 479, 487, 499, 523, 547, 587, 607, 631, 647, 683, 727, 827, 883, 907, 911, 919, 967, 991, 1019, 1031, 1051, 1087, 1123, 1171, 1303, 1327, 1423, 1499, 1511, 1523, 1531, 1567, 1571, 1667

Offset: 1

Author

M. F. Hasler, Sep 15 2015

Keywords

• nonn

Comments

Surprisingly, the variant A213900 with 11 instead of 12 has the same fixed points A000057 as the variant with 1 instead of 12, but other variants (A262212 - A262220 and A262211) have different sets of fixed points (A213891 - A213899 and this).

Crossrefs

Cf. A213648, A262212 - A262220, A213900, A262211; A000057, A213891 - A213899.

Programs

Mathematica

f[m_, n_] := Block[{c, k = 1}, c[x_, y_] := ContinuedFraction[x FromContinuedFraction[Join[{x}, Table[m, {y}], {x}]]]; While[First@ c[n, k] != Last@ c[n, k], k++]; k]; Select[Range[2, 1000], f[12, #] == # &] (* Michael De Vlieger, Sep 16 2015 *)

PARI

for(n=2,9999,n==A262211(n)&&print1(n","))